The access method Orthogonal Frequency Division Multiplexing (OFDM) is currently a popular modulation concept for next generation wireless systems e.g., 3GPP LTE (3rd Generation Partnership Project Long Term Evolution), IEEE WiMAX 802.16x, IEEE WiFi 802.11x, etc., as OFDM allows flexible resource allocation over wide bandwidth and practical channel equalization. However, the OFDM signal is characterized by large fluctuations of its power envelope that result in occasional spikes in the power of the signal. Therefore, OFDM systems should be designed allowing large power margins (referred to as power back-off), because the RF PA (Radio Frequency Power Amplifiers) as well as other digital and analog components need to be dimensioned in order to handle the occasional power peaks of the OFDM signal.
Various metrics have been introduced for the quantification of the dispersion of the histogram of the power envelope of OFDM signals. The most common one is the Peak to Average Power Ratio (PAPR) which is defined as
      PAPR    =                                                  y            ⁡                          (              t              )                                                ∞        2                    P        y              ,where y(t) is the transmitted baseband signal, Py is its power and ∥ ∥∞ is the infinite-norm operator.
For energy, cost, or space critical designs, such as mobile devices, the power back-off margins required by OFDM would lead to an inefficient solution. Therefore, a modified OFDM modulation, namely Discrete Fourier Transformation Spread Orthogonal Frequency Division Modulation (DFTS-OFDM) (also known as Single Carrier Orthogonal Frequency Division Modulation (SC-OFDM)), may be used to improve the efficiency of uplink transmissions, i.e., to reduce the PAPR. In a DFTS-OFDM transmitter a DFT precoder is placed before the IDFT precoder and a corresponding IDFT block it placed in the receiver. DFTS-OFDM leverages lower PAPR than OFDM, but at the same time it keeps the main advantage of OFDM which consists of simple equalization procedures. Therefore, the use of DFTS-OFDM leads to lower power back-off margins in the power amplifier (PA) and other components of the transmitter.
Further, the evolution of wireless communication systems towards the 4th Generation (4G) envisages also the adoption of spatial processing schemes for the multi-antenna (e.g. Multiple Input Multiple output, MIMO) transmission in the uplink. Various strategies have been proposed recently in order to exploit the multiple antennas for improving system performance including, e.g., STC (Space Time Coding), SFC (Space Frequency Coding), STFC (Space Time Frequency Coding) and LDC (Linear Dispersion Codes). In the following we implicitly assume the use of a specific type of LDC termed as SMLP (Spatial Multiplexing with Linear Precoding), because it is currently the main candidate for the uplink spatial processing of evolved LTE systems. SM (Spatial Multiplexing) consists of the simultaneous transmission of multiple data streams on the same time and frequency resources by taking advantage of the multiple transmit antennas. In order for the receiver to be able to separate the transmitted streams and correctly decode them the number of multiplexed streams must not be greater than the minimum of the number of transmit and receive antennas. Therefore, for SM it is necessary that both the transmitter and the receiver are provided with multiple antennas. In case of MIMO-DFTS-OFDM systems employing SM, an independent transmission chain is applied to each spatial stream, including DFT precoding, IDFT modulator and CP insertion. Each generated symbol is applied to a different transmit antenna, therefore every transmit antenna delivers the signal coming from a single specific spatial stream.
SMLP is a refined SM technique where each transmit antenna carries a linear combination of the spatial streams, instead of a single spatial stream as in standard SM. If the linear weights that define how each stream is mapped to each antenna are properly chosen, SMLP outperforms SM by focusing the transmit energy in the most favorable propagation subspaces of the channel. In a MIMO-DFTS-OFDM system the linear combination of the transmitted streams is usually carried out between the DFT precoders and the IDFT modulators.
SMLP potentially provides increased throughput for MIMO enabled devices and is foreseen as one of the major technical innovations for the uplink of forthcoming wireless telecommunication systems. In the following, a DFTS-OFDM system comprising of SMLP will be shortly termed as MIMO-DFTS-OFDM.
Turning to FIG. 1a showing a conventional MIMO DFTS-OFDM system with Ntx antennas 190 and Ns data streams 100 simultaneously transmitted on the same bandwidth. Ns DFT precoders 130 are simultaneously employed, each applied to a different stream. The DFT precoder 130 transforms the signal from the time domain to the frequency domain, therefore each output of the DFT precoder will be called subcarrier in the following. Hence in the figures, the subcarriers are denoted by arrows stemming out of the DFT precoder in the transmitter and as arrows stemming out of the IDFT demodulator in the receiver. Each DFT precoder 130 has size K and provides input to the Spatial Processing block 140 which may be built of a set of LP matrices B(k), each of them with dimensions (Ntx×Ns). The index k in B(k) provides the possibility to employ a different LP matrix on each subcarrier at the output of the DFT precoders, thus allowing subcarrier-adaptive LP in the most general case. Each LP matrix B(k) is fed with all the Ns outputs of the Ns precoders corresponding to the kth subcarrier and generates Ntx samples per subcarrier to be fed to the Ntx IDFT blocks as in FIG. 1a. Each IDFT block 160 has size M≧K and reverts the signal to the time domain to feed a dedicated RF section 180 and PA (power amplifier). By properly mapping the K scheduled subcarriers to the M inputs of the IDFT, it is possible to select the part of the available spectrum employed for transmission.
Further, the conventional MIMO DFTS-OFDM system of FIG. 1a comprises channel coding blocks 110. The input of each channel coding block consists of data streams 100, providing from some application running at the transmitter side or from a control service of the system (e.g., control signaling). The channel coding blocks 100 generate coded bits as an output, according to some suitable Forward Error Correction (FEC) Coding algorithm
The modulators 120 take as an input the sequence of the coded bits providing from the Channel Coding block 100 and maps them to a sequence of symbols. Each symbol consists of a possibly complex number belonging, e.g., to a widely employed signal constellation such as PAM, PSK, or QAM constellations. Accordingly, each modulated data stream is being input to one of the DFT pre-coders.
After the DFT precoder the Spatial Processing block 140 processes the various streams in the spatial domain and generates the signals to be fed to each transmit antenna 190. If LP is employed, the Spatial Processing block generates the Ntx outputs for each subcarrier by multiplying the corresponding Ns incoming streams with a Ntx×Ns matrix B(k), where k is the subcarrier index.
The subcarrier mapping block 150 is governed by resource mapping and scheduling functions in the upper layers of the system. It maps the output of the spatial processing block to a subset of the inputs of the IDFT block.
The Inverse Discrete Fourier Transformation (IDFT) 160 transforms the incoming signal from the frequency domain (subcarrier) to the time domain as described above. Since the length of the IDFT (M) is usually a power of 2, efficient algorithms such as IFFT (Inverse Fast Fourier Transformation) are widely and equivalently used. In order to simplify channel equalization at the receiver, it is common practice to replicate part of the transmitted OFDM symbol in the time domain.
This technique is widely known as Cyclic Prefix (CP) and is employed, e.g., in 3GPP LTE. Each signal is then fed to a respective antenna via a dedicated RF section comprising e.g. power amplifiers.
However, it can be shown by numerical simulations that the PAPR of a MIMO DFTS-OFDM is larger (worse) than in the case of a DFTS-OFDM system with equivalent bandwidth. This results in a larger power back-off for the PA and thus increased cost, energy consumption and space occupation, especially for the RF part of mobile devices. It is therefore of great importance to introduce technical features that are able to reduce the PAPR of the signal without hampering the advantages of the MIMO DFTS-OFDM system.
The theoretical reason why the PAPR of the MIMO DFTS-OFDM system increases with respect to conventional DFTS-OFDM is that BF combines independent data streams on each antenna. It is easy to show with the central limit theorem that the statistical distribution of the signal at the input of the PA of a MIMO system with BF tends to a Gaussian distribution for an increasing number of streams Ns. The Gaussian distribution is characterized by long queues and has thus bad PAPR properties. Therefore, peak power values and high PAPR are more likely to occur in the MIMO system with BF.
In addition to the aspects related to multi antennas, the evolution towards 4G systems (such as LTE-Advanced) requires the adoption of flexible resource allocation strategies over larger and possibly discontinuous spectrum windows referred to as multicarrier transmission. Each contiguous part of the assigned spectrum is called a carrier in the following of this description and it is uniquely identified by index n. One uplink scheme for multicarrier OFDM is referred to as NxDFTS-OFDM. NxDFTS-OFDM may be regarded as the natural evolution of SC-OFDM towards multicarrier transmission. In NxDFTS-OFDM an independent DFT precoder is assigned to each carrier or, more generally, to each assigned sub-band. A common IDFT is employed in the case of common PA for all the aggregated carriers.
FIG. 1b illustrates schematically a NxDFTS-OFDM system where N DFT precoders are simultaneously employed. The n-th DFT precoder has size Kn and its output is mapped to subcarriers dn . . . dn+Kn−1 at the input of a size M IDFT block. The underlying assumption is that each DFT is associated to a different carrier of a multicarrier system. However, the case where multiple DFTs are assigned to the same carrier is also covered by the same architecture.
The conventional NxDFTS-OFDM system comprises channel coding blocks 192, modulators 193, DFT-precoders 194, sub-carrier mappers 195, IDFT 196, a CP block 197 and a RF-block 198 with PA, which all have substantially the same functionality as the corresponding blocks of the MIMO DFTS-OFDM system shown in FIG. 1a. Further, in case of NxDFTS-OFDM, the subcarriers are mapped to N distinct clusters by the subcarrier mapper. Each cluster consists of all the Kn subcarrier relative to the n-th carrier.
It can be shown by numerical simulations that the PAPR of NxDFTS-OFDM is larger (worse) than in the case of a SC-OFDM system with equivalent bandwidth. This results in larger power back-off requirement for the PA similarly to the MIMO case. It is therefore of great importance to introduce technical features that are able to reduce the PAPR of the signal without hampering the advantages of the NxDFTS-OFDM system.